​BRINKLEY, JOHN, D.D. (1763–1835), bishop of Cloyne and first astronomer royal for Ireland, was born at Woodbridge in Suffolk, and owed to the influence and aid of Mr. Tilney of Harleston, under whose care he was educated, the means of supporting himself at Cambridge. He graduated at Caius College as senior wrangler and first Smith's prizeman in 1788, became a fellow of his college, proceeded M.A. in 1791, and D.D. in 1806. He contributed to the 'Ladies' Diary' from 1780 or 1781 to 1785, and acted as assistant at Greenwich while preparing for his degree. To Maskelyne's recommendation he owed his appointment, in 1792, as Andrews professor of astronomy in the university of Dublin, with the title, added on the death of Ussher, of 'Astronomer Royal for Ireland,' and the direction of the college observatory at Dunsink, near Dublin. Its sole equipment consisting at that time of a transit instrument, he had leisure to improve his knowledge of the higher mathematics, in which, as well as in acquaintance with the works of foreign analysts, he far excelled most of his contemporaries. The fruits of his inquiries were imparted to the Royal Irish Academy in a series of communications from 1797 to 1817, and to the Royal Society in 1807 in a paper entitled 'An Investigation of the General Term of an Important Series in the Inverse Method of Finite Differences' (Phil. Trans. xcvii. 114), of which the object was to surmount a difficulty remaining after Lagrange's investigation in the 'Berlin Memoirs' for 1772.

In the middle of 1808 a splendid altitude and azimuth circle, eight feet in diameter, ordered from Ramsden in 1788, and, after many delays, completed by his successor Berge, was set up at Dunsink, and Brinkley lost no time in turning it vigorously to account for the purposes of practical astronomy. His supposed discovery of an annual (double) parallax for α Lyræ of 2".52 was laid before the Royal Society in 1810 (Phil. Trans. c. 204), and he announced in 1814 (Trans. R. Irish Ac. xii. 33) similar and even larger results for several other stars. Their validity was disputed by Pond, and careful observations, made with a view to test it during several years, proved at Greenwich consistently adverse, at Dublin strongly confirmatory (Phil. Trans. cviii. 275, cxi. 327). In 1822 Brinkley described before the Royal Irish Academy a delicate instrumental investigation of solar nutation, heretofore known in theory only. If, he urged, his instrument were competent to exhibit the minute variations in the places of the stars produced by this cause, a fortiori it could be depended upon for the larger amounts ascribed to parallax (Trans. R. Irish Ac. xiv. 3, 1825). The argument seemed at the time unanswerable, and was fortified by his seemingly successful disengagement from the Greenwich observations themselves of a parallax for α Lyræ not differing sensibly from that inferred at Dublin (Mem. R. A. Soc. i. 329). The controversy, which was conducted on both sides with moderation and candour, terminated in 1824 with Brinkley's reassertion of his conclusion of fourteen years previously. Yet he was undoubtedly mistaken, although the source of his mistake remains obscure. The inquiry, however, was eminently useful in bringing about a closer scrutiny of instrumental defects and uranographical corrections, and so clearing the ground for further research. Brinkley's communications on the subject were honoured in 1824 by the Royal Society (of which body he had been elected a fellow in 1803) with the Copley medal. He presided over the Royal Irish Academy from 1822 until his death, and acted as vice-president of the Astronomical Society 1825-7, and as its president for the biennial period 1831-3.

In 1814 he published a new theory of astronomical refractions deduced from his own observations, with tables to facilitate their calculation (Trans. R. I. Ac. xii. 77) ; the same volume contains his catalogue of forty-seven fundamental stars. Fresh determinations by him of the obliquity of the ecliptic and of the precession of the equinoxes appeared respectively in 1819 and 1828 (Phil. Trans. cix. 241 ; Trans. R. I. Ac. xv. 39) ; and his constants of aberration and lunar nutation were adopted by Baily in the Astronomical Society's Catalogue, the former deduced from 2,633, the latter from 1,618 comparisons of various stars. He observed the great comet of 1819, and computed elements for it, and for the comet observed by Captain Hall at Valparaiso in 1821 (Quart. Jour. of Science, ix. 164 ; Phil. Trans. cxii. 50).

​His merits were recognised by ecclesiastical promotion. In 1608 he was collated to the prebend of Kilgoghlin and to the rectory of Derrybrusk; in 1808 he became archdeacon of Clogher, and on 28 Sept. 1826 bishop of Cloyne. The satisfaction of George IV with his reception at Trinity College, Dublin, is said to have been not unconnected with his final elevation. Thenceforth his episcopal duties engrossed all his attention, and the scientific activity, by which he had raised the little observatory at Dunsink to a position of first-rate importance, was brought to a close. After some years of failing health he died at his brother's house in Leeson Street, Dublin, on 14 Sept 1835, aged 72, and was buried in the chapel of Trinity College. A marble tablet erected to his memory in the cathedral of his diocese understates his age by three years. In character he was benevolent and disinterested.

He wrote (besides thirty-five contributions to learned collections, many of them separately reprinted) 'Elements of Astronomy,' Still used as a text-book in Dublin University, The work originated in his lectures to undergraduates, 1799-1808, which, at the request of the board, were published in the latter year, and again, with three additional chapters and an appendix, in 1813. Since then it has run through numerous editions, and obtained in 1671 renewed vitality in a careful recast by Drs. Stubbs and Brünnow. Brinkley's essay on the 'Mean Motion of the Lunar Perigee,' read before the Royal Irish Academy on 21 April 1817, obtained the Conyngham medal. He was one of the first to encourage the rising genius of Sir William Hamilton, his successor in the Andres chair of astronomy, and several of his letters are printed in the 'Life of Hamilton' by Graves (1882), i. 239-40, 297, 324. He was a botanist as well as an astronomer.